I notice it's transparent, so I thought maybe if I moved a notepad window over it, it wouldn't hide the calendar. But it does. How about a calendar that stays on top and is transparent, so I could see the calendar, and whatever else i'm using in that area.

You have several options in Right click -> Options -> General:
-> Set the position to "Always on Top"
-> Check "Click through (hold Shift-key down to deactivate)"
-> Change the normal opacity
-> Change the mouse over opacity